{"id":400,"date":"2023-07-03T01:21:27","date_gmt":"2023-07-03T01:21:27","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/"},"modified":"2023-07-03T01:21:27","modified_gmt":"2023-07-03T01:21:27","slug":"turunan-dari-kotangen-busur-hiperbolik","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/","title":{"rendered":"Turunan dari kotangen busur hiperbolik"},"content":{"rendered":"<p>Pada artikel ini kami menjelaskan cara menurunkan kotangen hiperbolik suatu fungsi. Selain itu, Anda akan dapat melihat contoh penyelesaian turunan kotatangen busur hiperbolik. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-arcocotangente-hiperbolica\"><\/span> Rumus turunan kotangen busur hiperbolik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan kotangen busur hiperbolik dari x adalah satu per satu dikurangi x kuadrat.<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42f0b83c10ae509a0cda1aa4abf25b92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{1-x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"411\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, <strong>turunan kotangen busur hiperbolik suatu fungsi<\/strong> sama dengan hasil bagi turunan fungsi tersebut dibagi satu dikurangi kuadrat fungsi tersebut.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ccadba79123a5f5e81d2b777d5cb9ba9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1-u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"411\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Perhatikan bahwa rumus kedua sama seperti rumus pertama tetapi menerapkan aturan rantai, sehingga rumus tersebut sebenarnya dapat dianggap sebagai rumus yang sama. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-de-larccotangente-hyperbolique.webp\" alt=\"berasal dari kotangen busur hiperbolik\" class=\"wp-image-2832\" width=\"391\" height=\"282\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Anda mungkin melihat di beberapa buku matematika bahwa turunan dari fungsi trigonometri invers jenis ini adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7c1e05f806ff6ead0b09d1af192c3345_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{-1}{x^2-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"114\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Namun jika dicermati, rumusnya sama, yang membedakan hanyalah pembilang dan penyebut pecahannya dikalikan -1. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-arcocotangente-hiperbolica\"><\/span><meta charset=\"utf-8\"> Contoh turunan dari kotangen busur hiperbolik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Contoh 1<\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5885f3abf1d025a4716d0233fdd5efda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(5x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"147\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam argumen kotangen busur hiperbolik kita mempunyai fungsi yang berbeda dari x, jadi kita perlu menggunakan rumus aturan rantai untuk menurunkannya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ccadba79123a5f5e81d2b777d5cb9ba9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1-u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"411\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Turunan dari 5x adalah 5, jadi masukkan angka 5 pada pembilang pecahan dan beri tanda minus 5x kuadrat pada penyebutnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-36c2652240dffeccc7b2094f68c570c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(5x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{5}{1-(5x)^2}}=\\cfrac{5}{1- 25x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"535\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Contoh 2<\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f6bb636493edeb7a8c2b9ee5e7890a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(e^{3x})\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Untuk menyelesaikan turunan fungsi tersebut, kita perlu menerapkan rumus turunan kotangen busur hiperbolik, yaitu sebagai berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ccadba79123a5f5e81d2b777d5cb9ba9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1-u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"411\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Dalam hal ini kita mempunyai fungsi majemuk, karena terdapat fungsi eksponensial dalam argumen fungsi trigonometri. Jadi kita perlu menggunakan aturan rantai untuk mencari turunan seluruh fungsi: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32563dc460ac67e1fbb529d3485e8297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(e^{3x}) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{3\\cdot e^{3x}}{1-\\left(e^{3x}\\right)^2}=\\cfrac{3e^{3x}}{1-3^{6x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"532\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"articulos-relacionados\"><\/span> Barang Serupa<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-tangen-busur-hiperbolik\/\">Turunan dari tangen busur hiperbolik<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung-hiperbolik\/\">Turunan dari garis singgung hiperbolik<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-kotangen-hiperbolik\/\">Turunan dari kotangen hiperbolik<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-arctangen\/\">Turunan dari arckotangen<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-arctangent-1\/\">Turunan dari arctangen<\/a><\/span><\/li>\n<li><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-kotangen\/\">berasal dari kotangen<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung\/\">turunan dari garis singgung<\/a><\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel ini kami menjelaskan cara menurunkan kotangen hiperbolik suatu fungsi. Selain itu, Anda akan dapat melihat contoh penyelesaian turunan kotatangen busur hiperbolik. Rumus turunan kotangen busur hiperbolik Turunan kotangen busur hiperbolik dari x adalah satu per satu dikurangi x kuadrat. Oleh karena itu, turunan kotangen busur hiperbolik suatu fungsi sama dengan hasil bagi turunan &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/\"> <span class=\"screen-reader-text\">Turunan dari kotangen busur hiperbolik<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[38],"tags":[],"class_list":["post-400","post","type-post","status-publish","format-standard","hentry","category-derivatif"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Turunan dari arckotangen hiperbolik - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Turunan dari arckotangen hiperbolik - Mathority\" \/>\n<meta property=\"og:description\" content=\"Pada artikel ini kami menjelaskan cara menurunkan kotangen hiperbolik suatu fungsi. Selain itu, Anda akan dapat melihat contoh penyelesaian turunan kotatangen busur hiperbolik. Rumus turunan kotangen busur hiperbolik Turunan kotangen busur hiperbolik dari x adalah satu per satu dikurangi x kuadrat. Oleh karena itu, turunan kotangen busur hiperbolik suatu fungsi sama dengan hasil bagi turunan &hellip; Turunan dari kotangen busur hiperbolik Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-03T01:21:27+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42f0b83c10ae509a0cda1aa4abf25b92_l3.png\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Turunan dari kotangen busur hiperbolik\",\"datePublished\":\"2023-07-03T01:21:27+00:00\",\"dateModified\":\"2023-07-03T01:21:27+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/\"},\"wordCount\":238,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Derivatif\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/\",\"url\":\"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/\",\"name\":\"Turunan dari arckotangen hiperbolik - 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Selain itu, Anda akan dapat melihat contoh penyelesaian turunan kotatangen busur hiperbolik. Rumus turunan kotangen busur hiperbolik Turunan kotangen busur hiperbolik dari x adalah satu per satu dikurangi x kuadrat. Oleh karena itu, turunan kotangen busur hiperbolik suatu fungsi sama dengan hasil bagi turunan &hellip; Turunan dari kotangen busur hiperbolik Selengkapnya &raquo;","og_url":"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/","article_published_time":"2023-07-03T01:21:27+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42f0b83c10ae509a0cda1aa4abf25b92_l3.png"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"1 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Turunan dari kotangen busur hiperbolik","datePublished":"2023-07-03T01:21:27+00:00","dateModified":"2023-07-03T01:21:27+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/"},"wordCount":238,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"articleSection":["Derivatif"],"inLanguage":"id","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/","url":"https:\/\/mathority.org\/id\/turunan-dari-kotangen-busur-hiperbolik\/","name":"Turunan dari arckotangen hiperbolik - 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